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Transition State Searching
Transition states are those regions of a potential surface through which a chemical reaction must pass to go from reactants to products. Ultimately, the transition state controls both the nature of the products of a reaction and the rate at which they are produced.
For potential surfaces of high dimensionality, e.g., molecular systems
with many atoms producing a large number of degrees of freedom, there is
no efficient way to find the best transition state between two configurations.
We are investigating new algorithms for finding transition states on high
Molecular Modeling of Polymer Systems 
Molecular modeling applies classical mechanics to molecular dynamics. Essentially, a potential field is set up for a molecule, and the classical equations of motion are integrated. The result is a trajectory of the motions of all of the individual atoms in time. While the results are deterministic, not probabalistic as quantum mechanics would dictate, for suitable systems reasonable results can be obtained. We are applying these techniques to large polymer systems composed of several thousand monomer units.
While the results of molecular dynamics calculations are appealing in
the sense that they give time dependent positions of the molecular components,
we have also demonstrated that care must be exercised in interpreting the
results. For instance, a lack of confinement of zero point energy
leads to excessive rate constants.
Polymer Fragment Size Distributions 
Based on a simplified model of transition state theory and branching
rations, we have developed a simple theory for predicting the size distribution
in fragments from thermal cracking of polymers. The model only depends
on factors such as the mass of the monomer units, and has product distributions
which are in agreement with molecular dynamics calculations.
Quantum Sieving of Hydrogen Isotopes in Nanostructures 
It is well known that hydrogen molecules can intercalate into carbon nanotubes. Much research has been done in this area with potential applications to hydrogen storage. Several years ago it was realized that the translational confinement of the molecules in the nanotubes produces zero-point energy in the newly bound translational coordinate. The zero-point energy is explicitly dependent on the mass of the molecule, and thus molecules with different masses effectively have different chemical potentials for absorption into the nanostructures.
What was not predicted at the time is that in addition to translational confinement, the rotational motions are also confined, and zero-point energy is introduced into these degrees of freedom as well. This zero-point energy differential becomes an additional component of the chemical potential, and produces an additional affinity for heavy isotopes to intercalate into the nanostructures.
Based on this principle, we have applied a semiclassical technique to
obtain the rotational eigenvalues as a function of nanotube size for a
model potential, and we have used the results to calculate the enrichment
of heavy isotopes bound to the substrate using statistical mechanical techniques.
Ozone Isotopic Enrichment [4-6]
Ozone formation shows a non standard isotopic enrichment in the heavy
isotopes of oxygen, where the enrichment is proportional not to the mass
difference in the isotopes, but on the presence of the isotopes and the
symmetry of the molecules formed. The theoretical basis for this
phenomenon remained elusive for three decades. In graduate work at
the California Institute of Technology, we developed a theory which correctly
accounted for the experimental phenomena.
We are investigating novel optical and material properties of structures
comprised of nanoparticles. These systems are being investigated
for possible mechanical and optical applications, including such novel
applications as wave guides.
Normal Mode Analysis of Polymer Systems[8-9]
Normal modes are the collective motion of a system near a local minimum. For a molecule, normal modes correspond to the vibrational coordinates. In addition to providing insight into the nature of the motions in the vicinity of the local minimum, knowledge of the frequencies of the normal modes allows the calculation of spectroscopic observables such as the infrared spectrum, thermodynamic observables such as the heat capacity, and rates for kinetic processes.
Recently, a new method has been developed which has enabled normal modes
of extremely large systems to be evaluated, eliminating spurious negative
eigenvalues which are obtained with traditional methods. We are applying
this method to a variety of complex systems.
 B.C. Hathorn, B.G. Sumpter, and D.W. Noid, Comparison of transition state theory rate constants for internal conformational motion with those obtained from Molecular Dynamics simulations. Polymer, 43, 615 (2002). postscript
 B.C. Hathorn, B.G. Sumpter, and D.W. Noid, On the Distribution of Fragment Sizes in the Fragmentation of Polymer Chains. Macromolecular Theory and Simulations, 10, 581 (2001). postscript
 B.C. Hathorn, B.G. Sumpter, and D.W. Noid, On the contribution of restricted rotors to quantum sieving of hydrogen isotopes. Physical Review A, 64, 022903, (2001). pdf
 B.C. Hathorn and R.A. Marcus, An intramolecular theory of the mass-independent isotope effect for ozone. I. Journal of Chemical Physics, 111, 4087 (1999). pdf
 B.C. Hathorn and R.A. Marcus, An intramolecular theory of the mass-independent isotope effect for ozone. II. Numerical applications at low pressures using a loose transition state, Journal of Chemical Physics, 113, 9497 (2000). pdf
 B.C. Hathorn and R.A. Marcus, Estimation of vibrational frequencies and vibrational densities of states in isotopically substituted nonlinear triatomic molecules, Journal of Physical Chemistry A, 105, 5586 (2001). pdf
 S.M. Mahurin, A. Mehta, B.C. Hathorn, B.G. Sumpter, D.W. Noid, K. Runge, and M.D. Barnes, Photonic ``polymers'': A new class of photonic wire structure from intersecting polymer-blend microspheres. Optics Letters, 27, 610 (2002).
 B.C. Hathorn, B.G. Sumpter, D.W. Noid and M.D. Barnes, Vibrational normal modes of polymer nanoparticle systems using the time averaged normal coordinate analysis method, Conference Proceedings, 6th World Multiconference on Systemics, Cybernetics and Informatics, 2002.
 B.C. Hathorn, B.G. Sumpter, D.W. Noid, R.E. Tuzun, and C. Yang, Computational Simulation of Polymer Particle Structures: Vibrational Normal Modes Using the Time Averaged Normal Coordinate Analysis Method, submitted.
 B.C. Hathorn, B.G. Sumpter, M.D. Barnes and D.W. Noid, Molecular Dynamics simulation of collinear nanoparticle collisions: reaction and scattering. J. Phys. Chem. B, 105, 11468 (2001).
 B.C. Hathorn, B.G. Sumpter, M.D. Barnes and D.W. Noid, Molecular Dynamics simulation of nanoparticle collisions: internal reorganization and translation-vibration coupling. Macromolecules, 35, 1102 (2002).
 B.C. Hathorn, B.G. Sumpter, M.D. Barnes and D.W. Noid Molecular Dynamics simulation of nanoparticle collisions: orbital angular momentum effects, Polymer, 43, 3115 (2002).
 B.C. Hathorn, B.G. Sumpter, and D.W. Noid, Theory of Unimolecular Reactions in Confined Volumes. submitted.